One of my great-grandfathers was a cobbler. Another was a carpenter. A third was a painter. The fourth had many jobs, including being a ferryman. They wanted better for their children than scraping together a living from poorly paid labour. They achieved it.

One of my grandfathers was a metal worker in a factory in Leeds where, among other things, he made petrol tanks for Spitfires. My other grandfather was a ladies' hairdresser in Portsmouth. The Rawnsleys and the Butlers had risen into the skilled working-classes. My paternal grandmother was a cake-maker and tailoress. My maternal grandmother sold drapery. They wanted better for their children. They achieved it.

My father was an engineer. My mother was a teacher. The Rawnsleys had now arrived in the middle-classes. The passage was not easy. My mum, evacuated during Hitler's Blitz, last saw her father when she was five and left school at 17 for teacher-training college. My dad left school at 13 and earned his qualifications at technical college, doing national service and from night school. They were both smart people with a strong work ethic, but neither had the opportunity to go to university. They wanted better for their children. They achieved it.

My sister and I went to Cambridge, the first of our family ever to enjoy the privilege of a higher education. I hope that would be a source of pride to my great-grandfathers, though some might argue that the rise of the Rawnsleys then went horribly wrong. All those generations of striving to advance up the social scale and I became a journalist.

I don't take you on this brief tour of my family tree in order to toot my own trumpet, but I don't blush to salute my forebears whose hard work, resourcefulness and ambition for their children built the foundations of the rewarding life that I enjoy today. Many other people of my age could tell similar tales of progress over the generations – "upward social mobility" in the jargon. My thoughts on it are prompted by the publication of a stonking "state of the nation" report by a commission chaired by Alan Milburn, the former Labour cabinet minister appointed by the government to be its "social mobility tsar". He's been given a silly title, but the report deserves to be taken extremely seriously. We already knew that social mobility was freezing up. And nearly everyone agreed that this is a bad thing. Bad for those trapped by the circumstances of their birth because it denies them the opportunity to flourish and fulfil their potential. Bad for society because disadvantage is perpetuated from parent to child, deepening inequality that, in a negative feedback loop, then makes it even harder for people to better themselves. As the report puts it: "Disadvantage and advantage cascade down the generations." Bad for the economy because untapped talent is left to waste. It is not only unjust. It is stupid.

The Milburn commission tells us that things are even more dismal than we thought. Social mobility is not just frozen, it is going into reverse. For the first time in a century, the squeeze on incomes means that the children of some of the middle class are threatened with a worse standard of living when they grow up than their parents.

In some quarters, this has been greeted with a fatalistic shrug. One argument is that the upward mobility enjoyed by my family was the result of a never-to-be-repeated change to society in the postwar years. As we shifted away from a predominantly industrial economy, there was a big expansion in clerical, managerial and professional roles. This opened the door for people to rise from blue-collar backgrounds into white-collar jobs. Put simply: there was a lot of social mobility in the decades immediately after 1945 because the middle class got a whole lot bigger. This can't happen again, so it is contended, and that is what mostly explains the freezing of social mobility in more recent decades. There is a finite amount of demand for lawyers, doctors, teachers, accountants and other middle-class professions. No more people can rise into the middle class because it is full up.

Worse, the pessimists continue, those who have attained a privileged position will do all they can to preserve their gains for their children. There is some obvious truth in this. A rich parent can buy an expensive house in the catchment area of a successful school. A poor parent can't. A rich parent has access to social and cultural networks that are closed to a poor parent. A rich parent will know someone who knows someone who can help their child into the internship that will launch them into a well-remunerated career. A poor parent can't do that for their children. My family's progress, an example of lively social mobility in the 20th century, can be advanced as an explanation for why it has died in the 21st. I may be a well-meaning, liberal-minded, caring, meritocratic sort of person. But when it comes to the crunch, my first priority will be maximising the life chances of my daughters. It is contended that those families who have climbed up the ladder will stamp on the fingers of anyone trying to rise after them. In this dark view, everyone says they believe in equality of opportunity, but no one in a position of any privilege actually wants to see it practised.

Phil Collins, a former adviser to Mr Milburn, has argued that this is why politicians are never really serious when they claim to want to see more social mobility. If they were, they would have to be brave enough to admit: "In the competition for the best jobs, my children's victory means the defeat of yours." This is the "snakes and ladders" or "zero-sum" take on social mobility. I like Mr Collins but I don't like his grim, self-fulfilling prophecy. Tell the prosperous that social mobility is their enemy and they are going to be all the more determined to entrench the advantages of their children. Tell them that social immobility threatens their own affluence in the long term and they may come to a different conclusion.

The Milburn report advances some mostly conventional ideas, though they are none the worse for that, about how to unlock social progress. Better schools with teachers focused on standards and closing attainment gaps. The right incentives to encourage people into employment. Accessible routes into work via education and training. It makes the excellent point that, for decades, politicians have been obsessed with universities to the detriment of "the other 50%" more likely to go into vocational education.

Those are the easier bits for the politicians to agree on, even if left and right will quarrel about the best method and where to find the money to fund it. One of the report's most important – but expensive, and therefore contentious – recommendations is for high-quality and universal childcare.

Children from disadvantaged backgrounds don't fall behind at school. They start behind. If birth is too often destiny, the best place to start tackling inequalities is the very earliest years of children's lives. It is no guarantee of closing the gap, but it can narrow it. There's an innovative American programme called Learning Dreams. Its insight is that the most effective way to encourage children to thrive in schools is to focus first on the parents. When parents are motivated to love learning as the route to attaining life goals, they are much more likely to pass that on to their children and inspire them to engage with education.

Behind it all is a giant question about the economy. We've seen a dramatic polarisation between highly rewarding work for those with the right skills and connections and badly paid work and little chance of social advancement for those without. Whether we can re-energise social mobility depends hugely on how Britain is going to earn its living in the future and what sort of jobs we are going to create. Living standards are not just about the size of energy bills. That is a trivial, passing spat between politicians compared with the question that really matters. Britain and the United States come bottom of the league table for social fluidity among developed nations. They are also the countries with the starkest inequalities. The best engine of social mobility is a high-value economy that creates many quality jobs across diverse sectors, spreading prosperity and opportunity more evenly. The alternative is the nightmarish future projected by the Milburn report, one in which even in economic recovery only the top slice of society prospers, the middle and bottom stagnate or fall even more behind and the rungs of the social ladder grow even further apart.

There might, just might, be a glimmer of light in the gloom. While a lack of life chances was just an issue for children from poor families, politicians could get away with sounding like they cared, but not applying themselves to do anything fundamental about it. When the middle classes start hurting and fearing that their children will slide down the scale, the politicians, themselves overwhelmingly middle class, are much likelier to sit up and really take notice.